论文标题
关于接触或点支持的潜力的一些最新结果
Some recent results on contact or point supported potentials
论文作者
论文摘要
我们引入了一些接触电势，可以写成Dirac Delta及其第一个衍生物的线性组合，即 $δ$ - $δ'$相互作用。经过一个简单的一般呈现，我们简要讨论了每个节点的$δ$ - $δ'$相互作用的一个维度周期电势。可以通过数值计算能量带对参数（增量系数）的依赖性。我们还研究了任意维度领域支持的$δ$ - $δ'$相互作用。该模型的球形对称性使我们能够在参数和维度方面获得有关绑定状态数量的严格结论。最后，使用$δ$ - $Δ'$相互作用用于近似核物理中广泛使用的潜力，并估计结合状态的总数以及某些能量最低的共振极的行为。
We introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the $δ$-$δ'$ interaction. After a simple general presentation in one dimension, we briefly discuss a one dimensional periodic potential with a $δ$-$δ'$ interaction at each node. The dependence of energy bands with the parameters (coefficients of the deltas) can be computed numerically. We also study the $δ$-$δ'$ interaction supported on spheres of arbitrary dimension. The spherical symmetry of this model allows us to obtain rigorous conclusions concerning the number of bound states in terms of the parameters and the dimension. Finally, a $δ$-$δ'$ interaction is used to approximate a potential of wide use in nuclear physics, and estimate the total number of bound states as well as the behaviour of some resonance poles with the lowest energy.
